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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 6.055J / 2.038J The Art of Approximation in Science and Engineering Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . Chapter 4 Symmetry Symmetry is often thought of as a purely geometric concept, but it is useful in a wide variety of problems. Whenver you can use symmetry, use it and will simplify the solution. The following sections illustrate symmetry in calculus, geometry, and heat transfer. 4.1 Calculus For what value of x is 3 x x 2 a maximum? The usual method is to take the derivative: d (3 x x 2 ) = 3 2 x = , dx whereupon x max = 3 / 2 . Although differentiating is a general method, its generality comes at a cost: that its results are often hard to interpret. One does the manipulations, and whatever formulas show up at the end, so be it. So, if you can find a simplification, you are likely to get a more insight into why the answer came out the way that it did....
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